In: Physics
A)
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass id riven by an external force equal to f(t) = 20 cos 3t use g=32 ft/s^2 for the acceleration due to gravity)
B)
A mass of 1 slug, when attached to a spring stretches it 2 feet and then comes to rest in the equilibrium position starting at t=0 an external force equal to f(t)=6 sin 4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. use g=32 ft/s^2 for the acceleration due to gravity.